For handwriting recognition integrating segmentation and classification, the underlying classifier is desired to give both high accuracy and resistance to outliers. In a previous evaluation study, the modified quadratic discriminant function (MQDF) proposed by Kimura et al. was shown to be superior in outlier rejection but inferior in classification accuracy as compared to neural classifiers. This paper proposes a learning quadratic discriminant function (LQDF) to combine the advantages of MQDF and neural classifiers. The LQDF achieves high accuracy and outlier resistance via discriminative learning and adherence to Gaussian density assumption. The efficacy of LQDF was Justified in experiments of handwritten digit recognition.